Skip to main content
Erschienen in: Queueing Systems 3-4/2022

19.03.2022

Multivariate M/G/1 systems with coupled input and parallel service

verfasst von: Michel Mandjes

Erschienen in: Queueing Systems | Ausgabe 3-4/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Excerpt

The M/G/1 queue, in which a queueing resource is fed by a Poisson stream of i.i.d. service requirements, is probably the most intensively studied of all queueing systems. One has succeeded in finding closed-form expressions for more performance measures that one could ever imagine; see, e.g., [6]. This makes it even more remarkable that by slightly generalizing the model, it becomes virtually impossible to analyze. In this contribution we consider one such generalization. …

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Asmussen, S.: Applied Probability and Queues. Springer, New York (2003) Asmussen, S.: Applied Probability and Queues. Springer, New York (2003)
2.
Zurück zum Zitat Avram, F., Palmowski, Z., Pistorius, M.: Exit problem of a two-dimensional risk process from the quadrant: exact and asymptotic results. Ann. Appl. Probab. 18, 2421–2449 (2008)CrossRef Avram, F., Palmowski, Z., Pistorius, M.: Exit problem of a two-dimensional risk process from the quadrant: exact and asymptotic results. Ann. Appl. Probab. 18, 2421–2449 (2008)CrossRef
3.
Zurück zum Zitat Avram, F., Palmowski, Z., Pistorius, M.: A two-dimensional ruin problem on the positive quadrant. Insur. Math. Econ. 42, 227–234 (2008)CrossRef Avram, F., Palmowski, Z., Pistorius, M.: A two-dimensional ruin problem on the positive quadrant. Insur. Math. Econ. 42, 227–234 (2008)CrossRef
4.
Zurück zum Zitat Baccelli, F.: Two parallel queues created by arrivals with two demands: the M/G/2 symmetrical case. Research Report, INRIA-Rocquencourt, 426 (1985) Baccelli, F.: Two parallel queues created by arrivals with two demands: the M/G/2 symmetrical case. Research Report, INRIA-Rocquencourt, 426 (1985)
5.
Zurück zum Zitat Badila, E., Boxma, O., Resing, J., Winands, E.: Queues and risk models with simultaneous arrivals. Adv. Appl. Probab. 46, 812–831 (2014)CrossRef Badila, E., Boxma, O., Resing, J., Winands, E.: Queues and risk models with simultaneous arrivals. Adv. Appl. Probab. 46, 812–831 (2014)CrossRef
6.
Zurück zum Zitat Cohen, J.W.: The Single Server Queue, 2nd edn. North-Holland, Amsterdam (1982) Cohen, J.W.: The Single Server Queue, 2nd edn. North-Holland, Amsterdam (1982)
7.
Zurück zum Zitat Cohen, J.W.: Analysis of Random Walks. IOS Press, Amsterdam (1992) Cohen, J.W.: Analysis of Random Walks. IOS Press, Amsterdam (1992)
8.
Zurück zum Zitat Collamore, J.: Hitting probabilities and large deviations. Ann. Probab. 24, 2065–2078 (1996)CrossRef Collamore, J.: Hitting probabilities and large deviations. Ann. Probab. 24, 2065–2078 (1996)CrossRef
9.
Zurück zum Zitat Dȩbicki, K., Dieker, T., Rolski, T.: Quasi-product forms for Lévy-driven fluid networks. Math. Oper. Res. 32, 629–647 (2007)CrossRef Dȩbicki, K., Dieker, T., Rolski, T.: Quasi-product forms for Lévy-driven fluid networks. Math. Oper. Res. 32, 629–647 (2007)CrossRef
10.
Zurück zum Zitat de Acosta, A.: Large deviations for vector-valued Lévy processes. Stoch. Process. Appl. 5, 75–115 (1994)CrossRef de Acosta, A.: Large deviations for vector-valued Lévy processes. Stoch. Process. Appl. 5, 75–115 (1994)CrossRef
11.
Zurück zum Zitat de Klein, S.: Fredholm integral equations in queueing analysis. PhD thesis, University of Utrecht (1988) de Klein, S.: Fredholm integral equations in queueing analysis. PhD thesis, University of Utrecht (1988)
12.
Zurück zum Zitat Foss, S., Korshunov, D., Palmowski, Z., Rolski, T.: Two-dimensional ruin probability for subexponential claim size. Probab. Math. Stat. 37, 319–335 (2017) Foss, S., Korshunov, D., Palmowski, Z., Rolski, T.: Two-dimensional ruin probability for subexponential claim size. Probab. Math. Stat. 37, 319–335 (2017)
13.
Zurück zum Zitat Kella, O.: Parallel and tandem fluid networks with dependent Lévy inputs. Ann. Appl. Probab. 3, 682–695 (1993)CrossRef Kella, O.: Parallel and tandem fluid networks with dependent Lévy inputs. Ann. Appl. Probab. 3, 682–695 (1993)CrossRef
14.
Zurück zum Zitat Kella, O., Whitt, W.: A tandem fluid network with Lévy input. In: Basawa, I., Bhat, U.N. (eds.) Queueing and Related Models, pp. 112–128. Oxford University Press, Oxford (1992) Kella, O., Whitt, W.: A tandem fluid network with Lévy input. In: Basawa, I., Bhat, U.N. (eds.) Queueing and Related Models, pp. 112–128. Oxford University Press, Oxford (1992)
15.
Zurück zum Zitat Koops, D., Boxma, O., Mandjes, M.: A tandem fluid network with Lévy input in heavy traffic. Queueing Syst. 84, 355–379 (2016)CrossRef Koops, D., Boxma, O., Mandjes, M.: A tandem fluid network with Lévy input in heavy traffic. Queueing Syst. 84, 355–379 (2016)CrossRef
16.
Zurück zum Zitat Lieshout, P., Mandjes, M.: Asymptotic analysis of Lévy-driven tandem queues. Queueing Syst. 60, 203–226 (2008)CrossRef Lieshout, P., Mandjes, M.: Asymptotic analysis of Lévy-driven tandem queues. Queueing Syst. 60, 203–226 (2008)CrossRef
17.
Zurück zum Zitat Mandjes, M., van Uitert, M.: Sample-path large deviations for tandem and priority queues with Gaussian inputs. Ann. Appl. Probab. 15, 1193–1226 (2005)CrossRef Mandjes, M., van Uitert, M.: Sample-path large deviations for tandem and priority queues with Gaussian inputs. Ann. Appl. Probab. 15, 1193–1226 (2005)CrossRef
18.
Zurück zum Zitat Szczotka, W., Kelly, F.: Asymptotic stationarity of queues in series and the heavy traffic approximation. Ann. Probab. 18, 1232–1248 (1990)CrossRef Szczotka, W., Kelly, F.: Asymptotic stationarity of queues in series and the heavy traffic approximation. Ann. Probab. 18, 1232–1248 (1990)CrossRef
Metadaten
Titel
Multivariate M/G/1 systems with coupled input and parallel service
verfasst von
Michel Mandjes
Publikationsdatum
19.03.2022
Verlag
Springer US
Erschienen in
Queueing Systems / Ausgabe 3-4/2022
Print ISSN: 0257-0130
Elektronische ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-022-09743-0

Weitere Artikel der Ausgabe 3-4/2022

Queueing Systems 3-4/2022 Zur Ausgabe

Premium Partner